Related papers: Multiscale Higher Order TV Operators for L1 Regula…
Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…
Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…
This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…
Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…
Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations require appropriate regularization functionals that model…
We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
Several bandwise total variation (TV) regularized low-rank (LR)-based models have been proposed to remove mixed noise in hyperspectral images (HSIs). Conventionally, the rank of LR matrix is approximated using nuclear norm (NN). The NN is…
Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved…
A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…
We propose novel high-order algorithms for a class of $\ell_p$-structured non-monotone variational inequalities. In particular, work by Diakonikolas et al. (2021), which introduced the weak Minty variational inequality (weak-MVI) setting,…
We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by…
MultiResolution Low-Rank decomposition is formulated for regularization of dynamic image sequences. The decomposition applies a local low-rank decomposition on a sequence of discrete wavelet transforms. Its effective formulation as a…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
The common graph Laplacian regularizer is well-established in semi-supervised learning and spectral dimensionality reduction. However, as a first-order regularizer, it can lead to degenerate functions in high-dimensional manifolds. The…
We study Tikhonov regularization for possibly nonlinear inverse problems with weighted $\ell^1$-penalization. The forward operator, mapping from a sequence space to an arbitrary Banach space, typically an $L^2$-space, is assumed to satisfy…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
Although regularization methods based on derivatives are favored for their robustness and computational simplicity, research exploring higher-order derivatives remains limited. This scarcity can possibly be attributed to the appearance of…
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…
In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…